Internal problem ID [4581]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x^{3}+\left (y+1\right )^{2} y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 89
dsolve(x^3+(y(x)+1)^2*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (-6 x^{4}-24 c_{1}\right )^{\frac {1}{3}}}{2}-1 \\ y \relax (x ) = -\frac {\left (-6 x^{4}-24 c_{1}\right )^{\frac {1}{3}}}{4}-\frac {i \sqrt {3}\, \left (-6 x^{4}-24 c_{1}\right )^{\frac {1}{3}}}{4}-1 \\ y \relax (x ) = -\frac {\left (-6 x^{4}-24 c_{1}\right )^{\frac {1}{3}}}{4}+\frac {i \sqrt {3}\, \left (-6 x^{4}-24 c_{1}\right )^{\frac {1}{3}}}{4}-1 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.685 (sec). Leaf size: 89
DSolve[x^3+(y[x]+1)^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+\frac {\sqrt [3]{-3 x^4+4+12 c_1}}{2^{2/3}} \\ y(x)\to -1+\left (-\frac {1}{2}\right )^{2/3} \sqrt [3]{-3 x^4+4+12 c_1} \\ y(x)\to \frac {1}{2} \left (-2-\sqrt [3]{-2} \sqrt [3]{-3 x^4+4+12 c_1}\right ) \\ \end{align*}